A hybrid numerical method for vibration analysis of linear multibody systems with flexible components

This paper presents a novel hybrid numerical method combining the transfer matrix method for multibody systems with the finite element method and the Craig-Bampton reduction method. In the proposed method, the multibody system is divided into two types of subsystems, depending on the shape and stiffness of each component. All the subsystems are independently analysed by the transfer matrix method for multibody systems or the finite element method and the Craig-Bampton reduction method. The whole system is recombined by deriving the relation equations of the connection points amongst subsystems. Then, the overall transfer equation and the eigenvalue equation of the whole system are obtained. Verifications on a simple system and rigid-flexible manipulator system show that the natural frequencies and modal shapes agree well with the finite element method. The dynamic model of the ultra-precision fly-cutting machine tool concerning the linearly elastic deformation of the fly-cutting head is established by the proposed method and validated by the experimental modal test. According to the comparison of computational speed with the finite element method, the proposed method has advantages in easy programming, low matrix order, low computational effort, and high applicability to the linear time-invariant mechanical system with flexible components.